Compression Spring Fundamentals
Compression springs are everywhere — from ballpoint pens to automotive suspensions. Designing one means balancing wire diameter, coil diameter, free length, and active coils to achieve your target spring rate and deflection without exceeding stress limits.
Key Formulas
Spring Rate (Stiffness)
k = Gd⁴ / (8D³Nₐ)
- k = spring rate (lbs/in or N/mm)
- G = shear modulus of wire material (psi or MPa)
- d = wire diameter
- D = mean coil diameter (OD – d)
- Nₐ = number of active coils
Spring Force
F = k × δ
where δ = deflection from free length
Shear Stress in Wire
τ = K_w × 8FD / (πd³)
K_w = Wahl correction factor = (4C – 1)/(4C – 4) + 0.615/C
C = spring index = D/d (target 4–12 for manufacturability)
Common Spring Wire Materials
| Material | Shear Modulus G (Mpsi) | Max Temp (°F) | Application |
|---|---|---|---|
| Music Wire (ASTM A228) | 11.5 | 250 | General purpose, highest strength |
| Hard Drawn (ASTM A227) | 11.5 | 250 | Non-critical, low cost |
| Oil Tempered (ASTM A229) | 11.5 | 350 | Automotive valves, medium stress |
| Chrome Silicon (ASTM A401) | 11.5 | 475 | High-temp, high-stress, shock loads |
| Stainless 302 (ASTM A313) | 10.0 | 550 | Corrosion resistance, food/medical |
| Stainless 17-7 PH | 10.5 | 600 | High-strength stainless |
| Phosphor Bronze (ASTM B159) | 6.0 | 200 | Electrical contacts, corrosion resistance |
| Beryllium Copper | 7.0 | 400 | Electrical contacts, non-magnetic |
| Inconel X-750 | 11.5 | 1100 | Extreme temperature, aerospace |
Design Guidelines
| Parameter | Recommended Range | Why |
|---|---|---|
| Spring Index (C = D/d) | 4 to 12 | Below 4: hard to coil. Above 12: may tangle/buckle |
| Active Coils (Nₐ) | 3 to 15 | Below 3: inconsistent rate. Above 15: may buckle |
| Free Length / D ratio | < 4 | Above 4: spring will buckle without a guide rod |
| Max shear stress | < 45% of tensile strength | Ensures fatigue life > 10⁶ cycles |
| Solid height clearance | 10–15% of working deflection | Never operate at solid height (coil bind) |
End Types
| End Type | Total Coils | Solid Height | Squareness |
|---|---|---|---|
| Open (plain) | Nₐ | d(Nₐ + 1) | Poor — spring leans |
| Closed (not ground) | Nₐ + 2 | d(Nₐ + 3) | Fair |
| Closed & Ground | Nₐ + 2 | d(Nₐ + 2) | Good — standard for precision |
Quick Design Procedure
- Define required force at working length and max deflection
- Calculate required spring rate: k = F / δ
- Choose wire material and diameter (from available stock sizes)
- Calculate mean coil diameter for target spring index (C = 6–8 is ideal)
- Calculate required active coils: Nₐ = Gd⁴ / (8D³k)
- Check stress at max deflection — must be below fatigue limit
- Verify solid height leaves adequate clearance
- Check for buckling if free length / D > 4
Related: Young’s Modulus Chart | Steel Numbering System